Multiobjective optimization and evolutionary algorithms

Contents

What is Multiobjective optimization

Multiobjective optimization (MO), also known as multicritera optimization is
an optimization of a vector function, where is a vector of parameters to the vector function , usually being a minimisation of components of with respect to Pareto efficiency.

Pareto efficiency, also known as Pareto optimality, is a best choice of criteria, such that no criterion must be worsened in order to better some another criterion. is Pareto optimal, iff does not exist .

What are Evolutionary Algorithms

Evolutionary Algorithms (EAs) are problem solving principles from nature applied to the metaheuristic search. Using mutation, crossover, and selection operators, stochastic search is developed to evolve better individuals in quest for (a) globally best individual(s).

When applying EAs to MO, multiple pareto optimal solutions are in the quest.
One of the possible EAs for exploring the MO search space is the Differential Evolution (e.g. jDE, 'rand/1/bin': ). The most known Genetic Algorithm (GA) for the MO is the Non-dominated Sorting Genetic Algorithm - II (NSGA-II) by Deb.

Performance Assessment of MOEAs

To assess an MOEA, test function suites are used, which comprise of several multiobjective test functions to solve.

When test function results are collected, performance metrics are used to assess the quality of an MOEA with respect to each performance metric.
If the preference of decision maker is same as with performance metric, then we can say that an MOEA has better quality (with respect to this preference).